The eikonal approximation (instanton technique) is applied to the problem of large fluctuations of the number of species in spatially homogeneous chemical reactions with the probability density distribution described by a master equation. For both autocatalytic and nonautocatalytic reactions, the analysis of the distribution about a stable stationary state and of the transitions between coexisting stable states comes, to logarithmic accuracy, to the analysis of Hamiltonian dynamics of an auxiliary dynamical system. The latter can be done explicitly in a few cases, including one-species systems, systems with detailed balance, and systems close to the bifurcation points where the number of the stable states changes. In the last case, the fluctuations display universal features, and, for saddle-node bifurcation points, the logarithm of the probability of escape from the metastable state (per unit time) is proportional to the distance to the bifurcation point (in the parameter space) raised to the power 3/2. We compare the eikonal approximation for the stationary distribution of a master equation to Monte Carlo numerical solutions for two chemical two-variable systems with multiple stationary states, where none of the cited restrictions exists. For one of the systems in the pattern of optimal paths we observe caustics emanating from the saddle point.

A quasi-two-dimensional set of electrons (1 < N < 10(9)) in vacuum, trapped in one-dimensional hydrogenic levels above a micrometer-thick film of liquid helium, is proposed as an easily manipulated strongly interacting set of quantum bits. Individual electrons are laterally confined by micrometer-sized metal pads below the helium. Information is stored in the lowest hydrogenic levels. With electric fields, at temperatures of 10(-2) kelvin, changes in the wave function can be made in nanoseconds. Wave function coherence times are 0.1 millisecond. The wave function is read out with an inverted dc voltage, which releases excited electrons from the surface.

We study dissipation effects for electrons on the surface of liquid helium, which may serve as qubits of a quantum computer. Each electron is localized in a 3D potential well formed by the image potential in helium and the potential from a submicron electrode submerged into helium. We estimate parameters of the confining potential and characterize the electron energy spectrum. Decay of the excited electron state is due to two-ripplon scattering and to scattering by phonons in helium. We identify mechanisms of coupling to phonons and estimate contributions from different scattering mechanisms. Even in the absence of a magnetic field we expect the decay rate to be < ∼ 10 4 s −1 . We also calculate the dephasing rate, which is due primarily to ripplon scattering off an electron. This rate is < ∼ 10 2 s −1 for typical operation temperatures.

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We analyze the rates of noise-induced transitions between period-two attractors. The model investigated is an underdamped oscillator parametrically driven by a field at nearly twice the oscillator eigenfrequency. The activation energy of the transitions is analyzed as a function of frequency detuning and field amplitude scaled by the damping and nonlinearity parameters of the oscillator. Both fourth-and sixth-order nonlinearities are taken into account. The parameter ranges where the system is bistable and tristable are investigated. Explicit results are obtained in the limit of small damping, or equivalently, strong driving, including scaling near bifurcation points.